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 Post subject: Higher order Pyraminx not possible?
PostPosted: Tue Jan 01, 2002 11:48 am 
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Joined: Tue Oct 09, 2001 6:14 am
Location: Orange County, CA, USA
It's an idea I've been kicking around for quite some Time and was wondering if anybody else attempted it.

Basically take a pyraminx design and attempt to add another "layer" to it, sort of the Revenge version of the Rubik's Cube but in tetrahedral configuration.

Unfortunately my attempts at designing one were stopped by a serious flaw in the design phase. In a Pyraminx the middle edge pieces overlap the central axis enough to allow for a tongue to be molded into the piece. With a higher order Pyraminx the lower edge piece (if you were to look at the Pyraminx from above0 would not have any overlap whatsoever. If you removed the edge pieces in question the shape traced would be a perfect hexagon, leave no room for a tongue to be molded into the pieces.

This is basically a show stopping flaw in the shape of the puzzle. While it would be possible to resize the pieces so that enough of an overlap is created, I think this detracts from the elegance and simplicity which seems to make puzzles so desirable.

With all of that rambling said, anybody have a study of what kind of mechanism WAS attempted in the following tetrahedron?

http://www.virtualpuzzlemuseum.com/pyramidpuzzles1of5.htm

Looks-wise this is exactly what I wanted to go for. From earlier discussion it was stated that a flaw in the mechanism caused this thing to cease production. But I would still like to see illustrations or diagrams of it to maybe see where it went wrong.


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 Post subject: higher order pyraminx is possible
PostPosted: Thu Jan 03, 2002 6:16 am 
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Joined: Wed Mar 15, 2000 9:11 pm
Location: Delft, the Netherlands
I believe an order 4 pyraminx with a fairly straightforward mechanism is possible.

The edge pieces do indeed overhang completely when you turn a size 3 corner. However this only ever happens on one side of the edge piece. Like the edges on a 4x4x4 cube, the pyraminx edges can never be flipped in place. The edge piece can therefore be asymetrical inside.

One of the inner surfaces must flat, to allow it to overhang, but on the other inside surface you can attach its tongue that sort of reaches in and around the adjacent vertex pieces. The middle pieces must of course be cut away enough to make room for such a tongue.

It is only when you get to the order 5 pyraminx when things become impossible because there the middle edge pieces would have to overhang on both sides.

I have not made am order 4 pyraminx, but I have thought about it enough to know how one would work. I would actually base the inner mechanism on a skewb. The free corners of the skewb are the face centres of the pyraminx, and the square faces become the other centre pieces. The axes of the fixed corners are extended to the tips of the pyraminx4.

Jaap


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 Post subject: Everything is posible
PostPosted: Thu Jan 03, 2002 7:27 am 
Everything is posible, at least in the case of this kind of puzzle, trust me on this. So the question is not is it posible but is it posible with such a system. For an order 4 tetrahedron I don't know if it is posible to use a normal spindle based system but I do know that it and all higer order tetrahederons are posible by useing a peice based system, i.e. each peice holds in the peices around it and is held in by them, fairly easily, it would be harder on even orders but still posible. This same system would work to make higher magnitude cubes, if it weren't for the fact my sculpting and plastic skills leave much to be disired I would have already prototyped it.
It is posible but I am at a loss to discribe this simple system.


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 Post subject: Is impossible possible?
PostPosted: Fri Jan 04, 2002 3:41 am 
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When I said in my post that:
"It is only when you get to the order 5 pyraminx when things become impossible because there the middle edge pieces would have to overhang on both sides."

I meant of course that it is impossible to use a straightforward tongue in groove system for this. The middle edge overhangs completely halfway through a turn so its inner surface could not have a tongue on that side. Since a different turn causes it to overhang on the other side as well, it cannot have a tongue at all. Using grooves on the piece instead is also not much help if you want the outside of the puzzle to look nice with straight cuts between the pieces.

I also have no doubt that theoretically it is possible to use some other kind of system (e.g. some mechanical locking mechanism inside the edge piece that locks it onto one if its adjacent edges when pressure is released from a switch on the other side and vice versa), but such mechanisms are hardly practical in my opinion.

A third option is to change the puzzle shape. As this changes the shape of the cutting plane, a tongue/groove system might work if the puzzle is closer to a sphere in shape. Alternatively change the distance between the cutting planes so the pieces overhang less. With the pyraminx of order 5+ you would tend to get extra pieces if you do only one of these, but you could do both and maybe get it to work.

Jaap


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 Post subject: Faith or certitude ?
PostPosted: Fri Jan 04, 2002 7:27 am 
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Joined: Fri Jan 04, 2002 7:27 am
Location: Munich, Germany
I find the idea interesting. I thought something similar in the past, but I classified it as an "intuition". Do you have you a base for your argument ?
It would be interesting to know more ...

Thanks !

Guido


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 Post subject: Higher order pyraminx thoughts
PostPosted: Sat Jan 05, 2002 6:22 pm 
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Joined: Tue Oct 09, 2001 6:14 am
Location: Orange County, CA, USA
Jaap, after your insightful mentioning that only one edge does not overlap, I began prototyping my own higher order pyraminx. The biggest problem I am having now is keeping the pieces simple.

As you have already pointed out, I discovered that even with just one higher order (I don't know what the original pyraminx's "order" is...) and just one edge overlapping, the conceptually easiest way to keep the piece from falling off is some sort of pressure regulated locking mechanism. Unfortunately this goes against the hope of having smooth visible surfaces between the turning planes. Besides, this would be for even higher order pyraminxes.

I've been working on a scheme similar to a Revenge's groove ball idea to make the pieces fit however. So far the idea looks promising. We'll see what happens.

Chris Witham, I would be very interested in seeing your design and perhaps comparing notes. While I don't consider myself an expert by any means when it comes to designing pieces and making molds, I have had some experience and ultimately I just want to see this puzzle happen, even in small batches. I'm sure you would be interested as well.


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 Post subject: larger pyraminx mechanism
PostPosted: Sun Jan 06, 2002 6:22 pm 
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Jin,

I call the normal pyraminx order 3 (3 pieces along the edge of the puzzle), so I call the next larger one order 4.

To keep the pieces relatively simple, without using some pressure-sensitive locking mechanism, I would use one mechanism inside another. Consider the 5x5x5 cube. Inside it has ball shaped 3x3x3 mechanism, with pieces that 'explode' outwards, allowing other pieces to be held between them in the outer shell.

I would (if I only could) build a larger pyraminx by using a skewb puzzleball inside. These pieces are all extended outwards, one set of triangles with rotatable vertices and tips, the squares expand to become the extra centre pieces, and the other set of triangles are expanded only a little bit (to allow a groove underneath) to become the face centres.

I would love to have this puzzle, but I just don't have the tools, materials, and skill to do this.

Jaap


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